Disclosed herein are embodiments of color scanner characterization, and more particularly, to systems and methods of performing a hierarchical subdivision of color space into sub-regions using principal component analysis to find axes of greatest variance in an input color set and generating a color transformation matrix for each sub-region using a weighting function.
Scanner characterization establishes the relationship, or mapping, between a scanner's device-dependent (scanner) color space and a device-independent colorimetric space, such as International Commission on Illumination CIE-XYZ color space. It is desirable to achieve very high accuracy scanner characterization.
Others have performed scanner characterization (sometimes called calibration) experiments. Ostromoukhov et al obtained results of 2.37 mean ΔE, in V. Ostromoukhov, R. D. Hersch, C. Péraire, P. Emmel, I. Amidror, “Two approaches in scanner-printer calibration: colorimetric space-based vs. closed-loop” in proc. SPIE 2170, pp. 133-142 1994. They noticed neighborhood effects, and attempted to reduce their impact by using large patches. Reduced accuracy in their results appear to be due to integrating cavity effect.
Hardeberg, J. Hardeberg, “Desktop Scanning to sRGB” in IS&T and SPIE's Device Independent Color, Color Hardcopy and Graphic Arts V, San Jose, Calif. (January 2000), optimized a third order (3×20) matrix, obtaining mean ΔE of 1.4 on two scanners, with less good results on others.
Previously, Haneishi et al., H. Haneishi, T. Hirao, A. Shimazu, and Y. Miyake, “Colorimetric precision in scanner calibration using matrices”, in Proceedings of IS&T and SID'S 3rd Color Imaging Conference: Color Science, Systems and Applications, pp. 106-108, Scottsdale, Ariz. (November 1995), had obtained mean ΔE=2 using a second (3×10) matrix regression. Rao, A. R. Rao, “Color calibration of a colorimetric scanner using non-linear least squares”, in Proc. IS&T's 1998 PICS Conference, Portland, Oreg. (May 1998), obtained similar values.
Hardeberg's thesis, J. Hardeberg, Acquisition and Reproduction of Colour Images: Colorimetric and Multispectral Approaches, Doctoral Dissertation, l'Ecole Nationale Superieure des Telecommunications (Paris 1999), describes an experiment (p. 37ff.) in which a single scanner is characterized with a mean ΔE of 0.92, a max of 4.67 and a 95th percentile of 2.25 on a set of 288 patches (the same set used to calibrate). He also characterized and tested on (disjoint) subsets (p. 51), and found that when he used 144 patches to train, and the other 144 to test, the mean ΔE rose to 0.96, but the max (of the test set) fell to 3.36 (the max ΔE for the training set was higher, at 3.9).
From a purely numerical, quality-of-fit standpoint, one of the best yet is described by Kotera, et al. in H. Kotera, A Ishige, H-S Chen and R. Saito “High Precision scanner/printer calibrations in sub-divided color spaces”, Journal of Imaging Science and Technology, Volume 43, number 2, March/April 1999. Kotera et al described experiments in which multiple (non-hierarchical) subdivisions of space, with no smooth transitioning across boundaries were tried. Regions were selected to have nearly identical numbers of input points within them. Their best results, with a cubic matrix, were 0.35 (RMS) and 1.58 (max). Kotera used only 240 input points, and then divided the input points spatially into 8 equal sized groups of about 30 points per group. The measure of quality is fit quality, that is, the difference between the input points and the fit evaluated at those inputs. Had Kotera increased the division to 12 groups averaging 20 points per group, the fit would have been perfect, since the number of points would be practically the same as the number of parameters (20 per separation). Kotera's subdivision of space was one of three forms based on simple divisions of L*a*b* space. The best results reported were for L*-C* division, where concentric shells of similar chroma were divided up by luminance. Kotera minimized the error between tristimulus (XYZ) values and RGB values converted through the fit matrix to tristimulus values.
It is desirable to provide scanner characterization that is accurate while providing a smooth transition between regions of color space using different matrices.